6.2 Early dynamical calculations

The earliest NS-NS merger calculations were performed in Newtonian gravity, sometimes with the addition of lowest-order 2.5PN radiation reaction forces, and typically assumed that the NS EOS was polytropic. Both Eulerian grid codes [214, 196, 215, 197, 278, 255, 201, 298] and Lagrangian SPH codes [234, 235, 236, 76, 330Jump To The Next Citation Point, 331Jump To The Next Citation Point] were employed, and GW signals were derived under the assumptions of the quadrupole formalism. Configurations in Newtonian gravity cannot collapse, so a stable (possibly hypermassive) remnant was always formed. For polytropic EOS models with adiabatic indices larger than the classical minimum for production of a Jacobi ellipsoid, Γ ≳ 2.6, remnants were typically triaxial and maintained a significant-amplitude GW signal until the end of the simulation. For simulations using smaller values of Γ, remnants rapidly relaxed to spheroidal configurations, quickly damping away the resulting GW signal. Mass loss from the central remnant was often quite significant, with thick accretion disks or completely unbound material comprising up to 10 – 20% of the total system mass

Mass loss was suppressed in numerical simulations by constructing irrotational, rather than synchronized, initial data. Irrotational flow is widely thought to be the more physically realistic case, since viscous forces are much too weak to synchronize a NS prior to merger [45, 146]. When irrotational NSs (which are counter-rotating in the corotating frame of the binary) first make contact, a vortex sheet forms. Since the low-density fluid layers at the contact surface are surrounded at first contact by the denser fluid layers located originally within each NS, the configuration is well understood to be Kelvin–Helmholtz unstable, resulting in rapid mixing through vortex production. Meanwhile, mass loss through the outer Lagrange points is hampered by the reduced rotational velocity along the outer halves of each NS.

The GW emission from these mergers is composed of a “chirp,” increasing in frequency and amplitude as the NSs spiral inward, followed by a ringdown signal once the stars collide and merge. In [330, 331], a procedure to calculate the energy spectrum in the frequency band was laid out, with the resulting signal following the quadrupole, point-mass power-law form up to GW frequencies characterizing the beginning of the plunge. Above the plunge frequency, a sharp drop in the GW energy was seen, followed in some cases by spikes at kHz frequencies representing coherent emission during the ringdown phase.


  Go to previous page Go up Go to next page